The Yankees need the Red Sox. The Redskins need the Cowboys. Republicans need Democrats. Matadors need bulls. And Google (Nasdaq: GOOG) needs Microsoft (Nasdaq: MSFT).

Rivals need each other because they push each other. Google has never needed a rival more than it needs one now. Microsoft, with Bing, can be that rival.

A better Bing means a better Google
What's wrong with Google? Nothing on the surface. The Big G has billions in cash, a dominant desktop- and mobile-search franchise, a clear winner in Android, and an emerging cloud-computing franchise in Google Apps. Everything's coming up roses for Google.

And that, Fool, should scare the beejeezus out of you.

Good times never last. Great managers know this, and they prepare for the worst even when all's well. Former Intel chief executive expressed this sentiment best when he said, "Only the paranoid survive." Google needs a healthy dose of paranoia.

There's plenty to be afraid of. Citing data from comScore and Citi, Search Engine Land reports that Bing reached an all-time high with 11.8% of searches in November. Mr. Softy's made gains in each of the past eight months. By contrast, partner Yahoo! has suffered declines since August.

Bing could see more gains in the months ahead. A new version allows users to rank results according to the likes and links shared by friends on Facebook. Microsoft is also working with Open Table (Nasdaq: OPEN) to allow Bing mobile-app users to make restaurant reservations directly from within local search results.

Google would love to include a similar feature in its own results. How do we know? The search king was prepared to pay $6 billion to acquire local-deals distributor Groupon.

Still searching for answers
Bing's existence is forcing us to once again ask what search should be. Is popularity really all that matters? Google would say yes; ranking high in its results is, in effect, like becoming the homecoming king or queen. The more links to your site (i.e., the more popular you are), the more you matter.

Trouble is, "popular" doesn't necessarily equal "relevant." Search spammers have for years used keywords and other "search-engine marketing" tricks to small-f fool algorithms into ranking their sites above legitimate alternatives.

Baidu (Nasdaq: BIDU) has courted trouble for mixing ads and search results, passing them off as one and the same when clearly they weren't. When Microsoft called Bing a "decision engine," it was a dig against Google and its peers and a reference to the spammers, a nod to relevance over popularity.

Start-ups are still beating this same drum. Consider Blekko. This venture-backed start-up adds what it calls "slashtags" to search strings in order to sharpen results. On-page tools also allow users to mark results as spam, making the algorithm smarter with each use.

How Google profits from others' innovations
All of this is good for Google. First, it shows that search innovation hasn't died. So long as there are innovations, critics will have a hard time making the case that Google should be broken up.

Second, it proves that Google needs developers who can think broadly about improving search. Competitive pressure has never let up. So long as this remains true, The Big G should be able to keep attracting top search talent. (After all, developers enjoy being on the front lines of a good fight.)

Talent and Big Ideas matter to investors, too. Why? Tech stocks do best when the underlying business is churning out innovations. In search, Google's mostly gotten past that point. A better Bing could ring in a new round of renovations -- and returns.

Now it's your turn to weigh in. Will anyone knock Google off its search perch? Please vote in the poll below, and then leave a comment to explain your thinking. You can also rate Google in Motley Fool CAPS.

Interested in more info on the stocks mentioned in this story? Add Google, Microsoft, Intel, Baidu, Yahoo!, comScore, or Open Table to your watchlist.

Google, Intel, and Microsoft are Motley Fool Inside Value picks. Baidu, Google, and Open Table are Motley Fool Rule Breakers recommendations. Motley Fool Options has recommended that subscribers purchase Intel calls, and a diagonal call position in Microsoft. Try any of our Foolish newsletter services free for 30 days.

Fool contributor Tim Beyers is a member of the Rule Breakers stock-picking team. He had stock and options positions in Apple and a stock position in Google at the time of publication. Check out Tim's portfolio holdings and Foolish writings, or connect with him on Twitter as @milehighfool. You can also get his insights delivered directly to your RSS reader. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a call option position in Intel and stock positions in Intel, Google, and Microsoft. The Fool is also on Twitter as @TheMotleyFool. Its disclosure policy couldn't be better, thanks.